Related papers: Spectral clustering and the high-dimensional stoch…
Significant progress has been made recently on theoretical analysis of estimators for the stochastic block model (SBM). In this paper, we consider the multi-graph SBM, which serves as a foundation for many application settings including…
Spectral clustering is a widely used method for community detection in networks. We focus on a semi-supervised community detection scenario in the Partially Labeled Stochastic Block Model (PL-SBM) with two balanced communities, where a…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks…
Community detection is a fundamental problem in network analysis, with applications in many diverse areas. The stochastic block model is a common tool for model-based community detection, and asymptotic tools for checking consistency of…
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…
Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…
The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual…
Spectral clustering is one of the most popular algorithms for community detection in network analysis. Based on this rationale, in this paper we give the convergence rate of eigenvectors for the adjacency matrix in the $l_\infty$ norm,…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…
Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
We consider the stochastic block model where connection between vertices is perturbed by some latent (and unobserved) random geometric graph. The objective is to prove that spectral methods are robust to this type of noise, even if they are…
In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the…
We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is…
In community detection on graphs, the semi-supervised learning problem entails inferring the ground-truth membership of each node in a graph, given the connectivity structure and a limited number of revealed node labels. Different subsets…
Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In…